Problem: Solve for $x$ and $y$ using elimination. ${3x+4y = 47}$ ${-3x+5y = -2}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $9y = 45$ $\dfrac{9y}{{9}} = \dfrac{45}{{9}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {3x+4y = 47}\thinspace$ to find $x$ ${3x + 4}{(5)}{= 47}$ $3x+20 = 47$ $3x+20{-20} = 47{-20}$ $3x = 27$ $\dfrac{3x}{{3}} = \dfrac{27}{{3}}$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {-3x+5y = -2}\thinspace$ and get the same answer for $x$ : ${-3x + 5}{(5)}{= -2}$ ${x = 9}$